21M BTC Max
There is a theoretical limit to the number of Bitcoins that can be mined - which is tied to the data structural limits of a blockchain. Only about six new blocks (a reference to a new transaction, a preceding transaction, and the answer to a complex mathematical problem) of bitcoins can be generated each hour. The Bitcoin system is designed to reduce the number of Bitcoins that can be generated by 50% every four years. About 94% of Bitcoins will have been mined by 2024, however assuming that processing / mining power remains constant the maximum of 21,000,000 may not be reached until more than a century after that point.